Finite Group Databasebeta

← C139×#8992 #48003588

Subgroups — C139×#8992 #48003588

Order 35584.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3103×C139C211yesmaximal, characteristic
2Q8×M16×C139C211yesmaximal, characteristic, complemented
3#1980×C139C211yesmaximal, characteristic
4C4×#103×C139C211yesmaximal, characteristic, complemented
5#1492×C139C211yesmaximal, characteristic
6#1303×C139C211yesmaximal, characteristic, complemented
7#1278×C139C211yesmaximal, characteristic, complemented
8#532×C139C2211yescharacteristic
9C2×C4×Q8×C139C2211yescharacteristic
10#481×C139—21no—
11#475×C139C411yescharacteristic, complemented
12#475×C139C411yescharacteristic, complemented
13#460×C139C411yescharacteristic, complemented
14#460×C139C411yescharacteristic, complemented
15#448×C139—21no—
16#446×C139—21no—
17#446×C139—22no—
18C8×Q8×C139—21no—
19C4×SD16×C139—21no—
20C4×SD16×C139—21no—
21#431×C139C2211yescharacteristic
22#423×C139—21no—
23#423×C139C2211yescharacteristic
24C2×#104×C139—21no—
25C2×#104×C139—21no—
26C2×#103×C139—21no—
27C4×M16×C139—21no—
28C4×M16×C139C2211yescharacteristic
29C2×C4×C8×C139C2211yescharacteristic
30C4×C4⋊C4×C139C2211yescharacteristic
31#340×C139—21no—
32D4⋊C8×C139—22no—
33C2×#41×C139—21no—
34C22×Q8×C139D411yescharacteristic
35C2×SD16×C139—21no—
36C2×SD16×C139—21no—
37C2×M16×C139—21no—
38C2×M16×C139D411yescharacteristic
39C2×M16×C139D411yescharacteristic
40C22×C8×C139—21no—
41C4⋊Q8×C139C2×C411yescharacteristic
42#127×C139C2×C411yescharacteristic
43#124×C139—21no—
44#121×C139—21no—
45#121×C139—21no—
46C4×Q8×C139—21no—
47C4×Q8×C139—21no—
48C4×Q8×C139C2×C411yescharacteristic
49C4×Q8×C139C2×C411yescharacteristic
50C4×Q8×C139D411yescharacteristic
51C4×Q8×C139D411yescharacteristic
52C4×D4×C139—21no—
53C4×D4×C139—21no—
54C2×C4⋊C4×C139—21no—
55C2×C4⋊C4×C139—21no—
56C2×C4⋊C4×C139D411yescharacteristic
57C2×C42×C139—21no—
58C2×C42×C139—21no—
59C2×C42×C139C2311yescharacteristic
60#106×C139—21no—
61#106×C139—21no—
62C4⋊C8×C139—22no—
63C4⋊C8×C139—22no—
64C4⋊C8×C139—21no—
65C4⋊C8×C139C2×C411yescharacteristic
66C4⋊C8×C139C2×C411yescharacteristic
67C4⋊C8×C139D412yes—
68#104×C139—42no—
69#104×C139—42no—
70#103×C139—24no—
71#103×C139—21no—
72#103×C139—21no—
73#102×C139—21no—
74#102×C139—21no—
75C22⋊C8×C139—21no—
76#97×C139—22no—
77#97×C139—21no—
78C4×C8×C139—22no—
79C4×C8×C139—21no—
80C4×C8×C139—21no—
81C4×C8×C139—21no—
82C4×C8×C139—21no—
83#95×C139—21no—
84#41×C139—41no—
85#41×C139—41no—
86#41×C139—41no—
87#41×C139—41no—
88C2×Q8×C139—21no—
89C2×Q8×C139—22no—
90C2×Q8×C139—21no—
91C2×Q8×C139—41no—
92C2×Q8×C139C22⋊C411yescharacteristic
93C2×Q8×C139C22⋊C411yescharacteristic
94C2×D4×C139—21no—
95C2×D4×C139—21no—
96C2×D4×C139—21no—
97C2×D4×C139—41no—
98C22×C4×C139—21no—
99C22×C4×C139—21no—
100C22×C4×C139—41no—
101C22×C4×C139—41no—
102C22×C4×C139C2×D411yescharacteristic
103C22×C4×C139C2×D411yescharacteristic
104C22×C4×C139#4111yescharacteristic
105SD16×C139—42no—
106SD16×C139—42no—
107M16×C139—21no—
108M16×C139—21no—
109M16×C139—21no—
110M16×C139—41no—
111M16×C139—41no—
112M16×C139SD1612yescomplemented
113C2×C8×C139—21no—
114C2×C8×C139—22no—
115C2×C8×C139—21no—
116C2×C8×C139—21no—
117C2×C8×C139—21no—
118C2×C8×C139—22no—
119C2×C8×C139—41no—
120C2×C8×C139—41no—
121C4⋊C4×C139—21no—
122C4⋊C4×C139—21no—
123C4⋊C4×C139—21no—
124C4⋊C4×C139—21no—
125C4⋊C4×C139—21no—
126C4⋊C4×C139—22no—
127C4⋊C4×C139—21no—
128C4⋊C4×C139—21no—
129C4⋊C4×C139—41no—
130C4⋊C4×C139C22⋊C411yescharacteristic
131C4⋊C4×C139C22⋊C411yescharacteristic
132C22⋊C4×C139—41no—
133C22⋊C4×C139—41no—
134C42×C139—21no—
135C42×C139—21no—
136C42×C139—21no—
137C42×C139—21no—
138C42×C139—41no—
139C42×C139—41no—
140C42×C139C22×C411yescharacteristic
141C42×C139C2×D411yescharacteristic
142C42×C139C2×D411yescharacteristic
143C42×C139#4111yescharacteristic
144C23×C139—41no—
145C23×C139#12111yescharacteristic
146Q8×C139—21no—
147Q8×C139—21no—
148Q8×C139—21no—
149Q8×C139—42no—
150Q8×C139—41no—
151Q8×C139—41no—
152Q8×C139#10412yescomplemented
153D4×C139—42no—
154D4×C139—41no—
155D4×C139—41no—
156D4×C139—41no—
157D4×C139—41no—
158D4×C139—81no—
159D4×C139—81no—
160C2×C4×C139—21no—
161C2×C4×C139—21no—
162C2×C4×C139—21no—
163C2×C4×C139—21no—
164C2×C4×C139—21no—
165C2×C4×C139—21no—
166C2×C4×C139—41no—
167C2×C4×C139—42no—
168C2×C4×C139—42no—
169C2×C4×C139—41no—
170C2×C4×C139—81no—
171C2×C4×C139—81no—
172C2×C4×C139—81no—
173C2×C4×C139—81no—
174C2×C4×C139—81no—
175C2×C4×C139C2×C22⋊C411yescharacteristic
176C2×C4×C139C4×D411yescharacteristic
177C2×C4×C139C4×D411yescharacteristic
178C2×C4×C139#12011yescharacteristic
179C2×C4×C139#12111yescharacteristic
180C2×C4×C139#12311yescharacteristic
181C2×C4×C139C2×SD1611yescharacteristic
182C2×C4×C139#13511yescharacteristic
183C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C139#13711yescharacteristic
185C8×C139—22no—
186C8×C139—42no—
187C8×C139—41no—
188C8×C139—41no—
189C8×C139—41no—
190C8×C139—42no—
191C22×C139—21no—
192C22×C139—21no—
193C22×C139—81no—
194C22×C139—81no—
195C22×C139—81no—
196C22×C139#38611yescharacteristic
197C22×C139#46011yescharacteristic
198C22×C139#46411yescharacteristic
199C4×C139—21no—
200C4×C139—22no—
201C4×C139—21no—
202C4×C139—21no—
203C4×C139—41no—
204C4×C139—41no—
205C4×C139—41no—
206C4×C139—82no—
207C4×C139—81no—
208C4×C139C2×#10411yescharacteristic
209C4×C139#42111yescharacteristic
210C4×C139C4×SD1611yescharacteristic
211C4×C139#44011yescharacteristic
212C4×C139#44811yescharacteristic
213C4×C139#44911yescharacteristic
214C2×C139—21no—
215C2×C139—21no—
216C2×C139—161no—
217C2×C139#187111yescharacteristic
218C2×C139#188011yescharacteristic
219C2×C139#188111yescharacteristic
220#8992C13911yesmaximal, characteristic, direct product factor, Sylow
221C139#899211yescharacteristic, direct product factor, Sylow
222#3103C2×C13911yescharacteristic
223Q8×M16C2×C13911yescharacteristic, complemented
224#1980C2×C13911yescharacteristic
225C4×#103C2×C13911yescharacteristic, complemented
226#1492C2×C13911yescharacteristic
227#1303C2×C13911yescharacteristic, complemented
228#1278C2×C13911yescharacteristic, complemented
229#532C22×C13911yescharacteristic
230C2×C4×Q8C22×C13911yescharacteristic
231#481—21no—
232#475C4×C13911yescharacteristic, complemented
233#475C4×C13911yescharacteristic, complemented
234#460C4×C13911yescharacteristic, complemented
235#460C4×C13911yescharacteristic, complemented
236#448—21no—
237#446—21no—
238#446—22no—
239C8×Q8—21no—
240C4×SD16—21no—
241C4×SD16—21no—
242#431C22×C13911yescharacteristic
243#423—21no—
244#423C22×C13911yescharacteristic
245C2×#104—21no—
246C2×#104—21no—
247C2×#103—21no—
248C4×M16—21no—
249C4×M16C22×C13911yescharacteristic
250C2×C4×C8C22×C13911yescharacteristic
251C4×C4⋊C4C22×C13911yescharacteristic
252#340—21no—
253D4⋊C8—22no—
254C2×#41—21no—
255C22×Q8D4×C13911yescharacteristic
256C2×SD16—21no—
257C2×SD16—21no—
258C2×M16—21no—
259C2×M16D4×C13911yescharacteristic
260C2×M16D4×C13911yescharacteristic
261C22×C8—21no—
262C4⋊Q8C2×C4×C13911yescharacteristic
263#127C2×C4×C13911yescharacteristic
264#124—21no—
265#121—21no—
266#121—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8C2×C4×C13911yescharacteristic
270C4×Q8C2×C4×C13911yescharacteristic
271C4×Q8D4×C13911yescharacteristic
272C4×Q8D4×C13911yescharacteristic
273C4×D4—21no—
274C4×D4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4D4×C13911yescharacteristic
278C2×C42—21no—
279C2×C42—21no—
280C2×C42C23×C13911yescharacteristic
281#106—21no—
282#106—21no—
283C4⋊C8—22no—
284C4⋊C8—22no—
285C4⋊C8—21no—
286C4⋊C8C2×C4×C13911yescharacteristic
287C4⋊C8C2×C4×C13911yescharacteristic
288C4⋊C8D4×C13912yes—
289#104—42no—
290#104—42no—
291#103—24no—
292#103—21no—
293#103—21no—
294#102—21no—
295#102—21no—
296C22⋊C8—21no—
297#97—22no—
298#97—21no—
299C4×C8—22no—
300C4×C8—21no—
301C4×C8—21no—
302C4×C8—21no—
303C4×C8—21no—
304#95—21no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309C2×Q8—21no—
310C2×Q8—22no—
311C2×Q8—21no—
312C2×Q8—41no—
313C2×Q8C22⋊C4×C13911yescharacteristic
314C2×Q8C22⋊C4×C13911yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4C2×D4×C13911yescharacteristic
324C22×C4C2×D4×C13911yescharacteristic
325C22×C4#41×C13911yescharacteristic
326SD16—42no—
327SD16—42no—
328M16—21no—
329M16—21no—
330M16—21no—
331M16—41no—
332M16—41no—
333M16SD16×C13912yescomplemented
334C2×C8—21no—
335C2×C8—22no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4C22⋊C4×C13911yescharacteristic
352C4⋊C4C22⋊C4×C13911yescharacteristic
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—21no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—41no—
360C42—41no—
361C42C22×C4×C13911yescharacteristic
362C42C2×D4×C13911yescharacteristic
363C42C2×D4×C13911yescharacteristic
364C42#41×C13911yescharacteristic
365C23—41no—
366C23#121×C13911yescharacteristic
367Q8—21no—
368Q8—21no—
369Q8—21no—
370Q8—42no—
371Q8—41no—
372Q8—41no—
373Q8#104×C13912yescomplemented
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4C2×C22⋊C4×C13911yescharacteristic
397C2×C4C4×D4×C13911yescharacteristic
398C2×C4C4×D4×C13911yescharacteristic
399C2×C4#120×C13911yescharacteristic
400C2×C4#121×C13911yescharacteristic
401C2×C4#123×C13911yescharacteristic
402C2×C4C2×SD16×C13911yescharacteristic
403C2×C4#135×C13911yescharacteristic
404C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
405C2×C4#137×C13911yescharacteristic
406C8—22no—
407C8—42no—
408C8—41no—
409C8—41no—
410C8—41no—
411C8—42no—
412C22—21no—
413C22—21no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22#386×C13911yescharacteristic
418C22#460×C13911yescharacteristic
419C22#464×C13911yescharacteristic
420C4—21no—
421C4—22no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—82no—
428C4—81no—
429C4C2×#104×C13911yescharacteristic
430C4#421×C13911yescharacteristic
431C4C4×SD16×C13911yescharacteristic
432C4#440×C13911yescharacteristic
433C4#448×C13911yescharacteristic
434C4#449×C13911yescharacteristic
435C2—21no—
436C2—21no—
437C2—161no—
438C2#1871×C13911yescharacteristic
439C2#1880×C13911yescharacteristic
440C2#1881×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139#120
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
socleC22×C139#386
prime radical#532×C139C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. Q8×M16×C139C2semidirect
4. C4×#103×C139C2semidirect
6. #1303×C139C2semidirect
7. #1278×C139C2semidirect
11. #475×C139C4semidirect
12. #475×C139C4semidirect
13. #460×C139C4semidirect
14. #460×C139C4semidirect
112. M16×C139SD16semidirect
152. Q8×C139#104semidirect
220. #8992C139direct (N × H)
221. C139#8992direct (N × H)
223. Q8×M16C2×C139semidirect
225. C4×#103C2×C139semidirect
227. #1303C2×C139semidirect
228. #1278C2×C139semidirect
232. #475C4×C139semidirect
233. #475C4×C139semidirect
234. #460C4×C139semidirect
235. #460C4×C139semidirect
333. M16SD16×C139semidirect
373. Q8#104×C139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3103×C1392
Q8×M16×C1392
#1980×C1392
C4×#103×C1392
#1492×C1392
#1303×C1392
#1278×C1392
#8992139